Spin dynamics of a J ₁-J ₂-K model for the paramagnetic phase of iron pnictides

We study the finite-temperature spin dynamics of the paramagnetic phase of iron pnictides within an antiferromagnetic J ₁-J ₂ Heisenberg model on a square lattice with a biquadratic coupling -K ⁽S _i ^•S _j ⁾2 between the nearest-neighbor spins. Our focus is on the paramagnetic phase in the parameter regime of this J ₁-J ₂-K model where the ground state is a (π,0) collinear antiferromagnet. We treat the biquadratic interaction via a Hubbard-Stratonovich decomposition and study the resulting effective quadratic-coupling model using both modified spin wave and Schwinger boson mean-field theories; the results for the spin dynamics derived from the two methods are very similar. We show that the spectral weight of dynamical structure factor S(q,ω) is peaked at ellipses in the momentum space at low excitation energies. With increasing energy, the elliptic features expand towards the zone boundary and gradually split into two parts, forming a pattern around (π,π). Finally, the spectral weight is anisotropic, being larger along the major axis of the ellipse than along its minor axis. These characteristics of the dynamical structure factor are consistent with the recent measurements of the inelastic neutron scattering spectra of BaFe ₂As ₂ and SrFe ₂As ₂.